We have analyzed several aspects of Pearson random walks that are useful in determining the space groups of molecules from crystallographic data. In particular, an exact expression has been found for the probability density of the projection of a Pearson random walk near maximum extension. Useful numerical methods have been developed for calculating the projection density as well as the end-to-end density for Pearson random walks with one or two outstandingly long steps included among a larger number of smaller steps.